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Compl Integ Trans Syste 26843 pair #381744689
details
property
value
status
complete
benchmark
realbubble.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.9922978878 seconds
cpu usage
7.20205759
max memory
4.3040768E8
stage attributes
key
value
output-size
119695
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 544 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 1319 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realbubble_start(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb0_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_bb0_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_1(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_1(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_2(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_2(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_3(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_3(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_4(v_length - 1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_4(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_5(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_5(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_6(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_6(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_7(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_7(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_8(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_8(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_9(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_9(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_10(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_10(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb1_in(v_1, v_26, v_1, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_bb1_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb2_in(v_1, v_26, v_i_0, 0, v_length, 0, v_test_1)) :|: v_i_0 > 0 eval_realbubble_bb1_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb8_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_i_0 <= 0 eval_realbubble_bb2_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb3_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_j_0 < v_i_0 eval_realbubble_bb2_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_j_0 >= v_i_0 eval_realbubble_bb3_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb4_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: nondef_1 > nondef_2 eval_realbubble_bb3_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb5_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_0)) :|: nondef_1 <= nondef_2 eval_realbubble_bb4_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb5_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, 1)) :|: TRUE eval_realbubble_bb5_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb2_in(v_1, v_26, v_i_0, v_j_0 + 1, v_length, v_test_1, v_test_1)) :|: TRUE eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb8_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_test_0 >= 0 && v_test_0 <= 0 eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb7_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_test_0 < 0 eval_realbubble_bb6_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb7_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: v_test_0 > 0 eval_realbubble_bb7_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_31(v_1, v_i_0 - 1, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_31(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_32(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_32(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_bb1_in(v_1, v_26, v_26, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE eval_realbubble_bb8_in(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1) -> Com_1(eval_realbubble_stop(v_1, v_26, v_i_0, v_j_0, v_length, v_test_0, v_test_1)) :|: TRUE The start-symbols are:[eval_realbubble_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 253*ar_1 + 36*ar_1^2 + 18) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealbubblestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubblebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble4(ar_1 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble9(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubble10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubble10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb1in(ar_0, ar_1, ar_0, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb2in(ar_0, ar_1, ar_2, 0, 0, ar_5, ar_6)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrealbubblebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealbubblebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_2 ] (Comp: ?, Cost: 1) evalrealbubblebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealbubblebb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ h >= i + 1 ]
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